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Inverse Hyperbolic Cotangent Calculator
Calculate the inverse hyperbolic cotangent of a number
The calculator will find the inverse hyperbolic cotangent of the given value.
The inverse hyperbolic cotangent $$$y=\coth^{-1}(x)$$$ or $$$y=\operatorname{acoth}(x)$$$ or $$$y=\operatorname{arccoth}(x)$$$ is such a function that $$$\coth(y)=x$$$.
It can be expressed in terms of elementary functions: $$$y=\coth^{-1}(x)=\frac{1}{2}\ln\left(\frac{x+1}{x-1}\right)$$$.
The domain of the inverse hyperbolic cotangent is $$$(-\infty,-1)\cup(1,\infty)$$$, the range is $$$(-\infty,0)\cup(0,\infty)$$$.
It is an odd function.
Related calculator: Hyperbolic Cotangent Calculator
Your Input
Find $$$\operatorname{acoth}{\left(5 \right)}$$$.
Answer
$$$\operatorname{acoth}{\left(5 \right)}\approx 0.202732554054082$$$A
For graph, see the graphing calculator.